# Will 2 particles with paths crossed collide?

## Homework Statement

The first particle A is starting at origin and it has a velocity vector with magnitude 10km/h and moves at an angle of 30 degrees relative to y axis. The second particle B is starting at (0,5) and it has velocity vector with magnitude 8km/h and moves at an agle of 60 degrees relative to y axis. Will these 2 particles colide, and if not, what is the minimal distance they will be at?

## The Attempt at a Solution

I found the velocity vectors with given angles/magnitudes. I'm not sure what to do now.

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The particles will collide at time where both at x and y displacement are equal if time t exist.

Yeah I got position vector rA and rB from formula r(t)=v*t, where r and v are vectors. They have this form rA=x*t*i + y*t*j where i and j are unit vectors. What do I get from equatting positions, how do I calculate time from that?

The correct answer is that they don't collide and minimal distance is 1.8km. So does it really make sense to equate postitions if we're not 100% sure they'll collide? Im really confused :/

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Find time in y direction where both displacements are equal. Then on x direction or component. If both time are equal then they meet.

TSny
Homework Helper
Gold Member
jefer,

Have you studied the concept of relative velocity? If so, what is the velocity of B relative to A?

vela
Staff Emeritus